Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Problem Statement:**
Find the equation of the line in slope-intercept form parallel to \( 5x + 6y = -2 \) and goes through the point \((6, -3)\).
**Solution:**
To find the equation of the desired line, we first need to determine the slope of the given line \( 5x + 6y = -2 \). We can rewrite this equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope.
1. **Rearrange the given equation:**
\[
6y = -5x - 2
\]
\[
y = -\frac{5}{6}x - \frac{1}{3}
\]
The slope of the given line is \( m = -\frac{5}{6} \).
2. **Since parallel lines have the same slope, the slope of the line we need to find is also \( m = -\frac{5}{6} \).**
3. **Use the point-slope form to find the equation of the new line:**
The point-slope form is \( y - y_1 = m(x - x_1) \), where \((x_1, y_1)\) is the point the line passes through.
Substituting \( m = -\frac{5}{6} \), \( x_1 = 6 \), and \( y_1 = -3 \):
\[
y + 3 = -\frac{5}{6}(x - 6)
\]
\[
y + 3 = -\frac{5}{6}x + 5
\]
\[
y = -\frac{5}{6}x + 5 - 3
\]
\[
y = -\frac{5}{6}x + 2
\]
Therefore, the equation of the line in slope-intercept form is:
\[
y = -\frac{5}{6}x + 2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99db74cb-a52b-4540-9e19-530fc4ba7537%2F15fd7401-2a2b-4302-b42e-607183702182%2Fclwiuu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the equation of the line in slope-intercept form parallel to \( 5x + 6y = -2 \) and goes through the point \((6, -3)\).
**Solution:**
To find the equation of the desired line, we first need to determine the slope of the given line \( 5x + 6y = -2 \). We can rewrite this equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope.
1. **Rearrange the given equation:**
\[
6y = -5x - 2
\]
\[
y = -\frac{5}{6}x - \frac{1}{3}
\]
The slope of the given line is \( m = -\frac{5}{6} \).
2. **Since parallel lines have the same slope, the slope of the line we need to find is also \( m = -\frac{5}{6} \).**
3. **Use the point-slope form to find the equation of the new line:**
The point-slope form is \( y - y_1 = m(x - x_1) \), where \((x_1, y_1)\) is the point the line passes through.
Substituting \( m = -\frac{5}{6} \), \( x_1 = 6 \), and \( y_1 = -3 \):
\[
y + 3 = -\frac{5}{6}(x - 6)
\]
\[
y + 3 = -\frac{5}{6}x + 5
\]
\[
y = -\frac{5}{6}x + 5 - 3
\]
\[
y = -\frac{5}{6}x + 2
\]
Therefore, the equation of the line in slope-intercept form is:
\[
y = -\frac{5}{6}x + 2
\]
Expert Solution
Step 1
NOTE: Refresh your page if you can't see any equations.
.
solve for y
here coefficient of x is -5/6
so the slope of the given line is
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